Question

Q. 22 9^x+2 = 720 + 9^x , find the value of x

Answer 1

Question :–

▪︎ If $\: \: { \bold{ {9}^{x + 2} = 720 + {9}^{x} }}$ then find the value of x .

ANSWER :–

$\\ \to \: { \boxed{ \bold{ x = 1}}}$

EXPLANATION :–

GIVEN :–

$\\ \implies \: { \bold{ {9}^{x + 2} = 720 + {9}^{x} }}$

TO FIND :–

• Value of x

SOLUTION :–

$\\ \implies \: { \bold{ {9}^{x + 2} = 720 + {9}^{x} }}$

$\\ \implies \: { \bold{ {9}^{x + 2} - {9}^{x} = 720 }}$

$\\ \implies \: { \bold{ {9}^{x} ( {9}^{2} - 1) = 720 }}$

$\\ \implies \: { \bold{ {9}^{x} (81 - 1) = 720 }}$

$\\ \implies \: { \bold{ {9}^{x} (80) = 720 }}$

$\\ \implies \: { \bold{ {9}^{x} = \cancel \frac{720}{80} }}$

$\\ \implies \: { \bold{ {9}^{x} = 9 }}$

$\\ \implies \: { \bold{ {9}^{x} = {(9)}^{1} }}$

▪︎ Now let's compare –

$\\ \implies \: { \boxed{ \bold{ x = 1}}}$

USED IDENTITIES :–

$\\ \: { \bold{ (1) \: \: {(a)}^{b + c} =( {a}^{b}) .({a}^{c})}}$

$\\ \: { \bold{ (2) \: \: if \: \: {(a)}^{b } = ({a}^{c}) \: \: then \: \: }} { \boxed{ \bold{b = c}}}$